Calculus

Hi~ Thank you for your help!
I was trying to work on a problem about Taylor series, but i don't think im approaching the problem the right way.
I have to find the fifth order Taylor polynomial and Taylor series for the function f(x) at x = 0.
f(x) = 1/(x+2)
I tried to just write out the first and second and third derivatives, and this was fine, but then i got to the fourth and fifth derivatives and the quotient rule made the derivative look really confusing....is there a better way to approach this problem?

I might be doing this totally wrong since we just started learning Taylor series today in class, so any advice is much appreciated.

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  1. It turns out that if you had done your derivatives correctly, you would have found the rule:
    for f(x)=1/(x+2)
    f(n)(x) = (-1)(n)n!/(x+2)n+1

    I got f(5)(x)=-120/(x+2)6.

    Hope that helps.

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